# If sin a = (3/14) find cos a and tan (a)

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sin(a) = 3/14

We need to determine sin(a) and tan(a).

We will use the trigonometric properties to find cos(a) and tan(a).

We know that: sin^2 x + cos^2 a = 1

Let us substitute with sin(1) = 3/14.

==> (3/14)^2 + cos^2 a = 1

--< cos^2 a = 1- (9/196)

==> cos^2 a = 187/ 196

**==> cos(a) = sqrt(187) / 14**

Now let us calculate tan(a).

From trigonometric properties, we know that tan(a) = sin(a)/cos(a).

==> tan(a) = (3/14) / ( sqrt187/ 14)

= 3/sqrt187

**==> tan(a) = 3/ sqrt(187)**

We know that (tan x)^2 = 1/[1 + (cos x)^2] (1)

But, form enunciation, we know the value of sine function, and not cosine. This is not a problem, though.

We can determine the value of cosine function, using the fundamental formula of trigonometry:

(cos x)^2 = 1 - (sin x)^2

We'll substitute sin x by it's given value:

(cos x)^2 = 1 - (3/14)^2

(cos x)^2 = 1 - 9/196

(cos x)^2 = 187/196 (2)

We'll substitute (2) in (1) by the resulted value:

(tan x)^2 = 1/(1+ 187/196)

(tan x)^2 = 196/383

tan x = sqrt 196/383

tan x = 14/sqrt383

**tan x = 14sqrt383/383**